Accurate transonic wave drag prediction using simple physical models

Abstract

A new method is presented to compute the transonic wave drag of airfoils. Coupled with an inverse boundary-layer procedure, the calculated results have an accuracy comparable to experiments. The method is robust and easy to handle without the necessity of tuning; hence, it is an excellent engineering tool for supercritical airfoil design. The inviscid flowfield is assumed to be governed by the full potential equation except at the shock. The solution is obtained by a finite-difference method. At shock points, a shock operator is introduced; it satisfies the kinematic Prandtl relation for normal and oblique shocks, which is the consistent condition for the velocity potential. For each streamline behind the shock, an entropy correction is calculated by the Rankine-Hugoniot equations. The wave drag is given by integrating the entropy rise along the shock. The computational mesh, formed by incompressibl e stream and potential lines, allows easy coupling of the boundary-layer solution at the airfoil and wake. The H-type singularity at the incompressible stagnation point is handled by a finite-volume procedure. For better physical pressure and drag solutions, the condition of the normal shock has to be altered due to the boundary layer. Therefore, an analytic model of the inviscid interference region was developed and the essential features are embedded in the numerical procedure.